Theorem 5.1 [1]}
Let \(X\)  be a separable Banach space. Let \(\mathcal {U}\)  be a set of measurable functions \(u:(0,T)\rightarrow X\) , let \(\mathcal {G} : X \rightarrow [0, +\infty ]\)  be a normal coercive integrand and \(g : X \times X \rightarrow [0, +\infty ]\)  be a l.s.c. pseudo-distance compatible with \(\mathcal {G}\) . Assume moreover that
\(\sup _{u\in \mathcal {U}}\int _0^T\mathcal {G}(u(t))\,\mathrm {d}t<+\infty \) 
